TÜSİAD-KOÇ UNIVERSITY ECONOMIC RESEARCH FORUM WORKING PAPER SERIES

CYCLICAL DYNAMICS OF INDUSTRIAL PRODUCTION AND EMPLOYMENT:

MARKOV CHAIN-BASED ESTIMATES AND TESTS

Sumru Altuğ Barış Tan

Gözde Gencer

Working Paper 1101 January 2011

http://www.ku.edu.tr/ku/images/EAF/erf_wp_1101.pdf

TÜSİAD-KOÇ UNIVERSITY ECONOMIC RESEARCH FORUM Rumeli Feneri Yolu 34450 Sarıyer/Istanbul

Cyclical Dynamics of Industrial Production and Employment:

Markov Chain-based Estimates and Tests

Sumru Altug Barıs TanKoc University and CEPR Koc University

Gozde GencerYapıkredi Bank∗

January 24, 2011

Abstract

This paper characterizes the business cycle as a recurring Markov chain for a broadset of developed and developing countries. The objective is to understand differences incyclical phenomena across a broad range of countries based on the behavior of two keyeconomic times series – industrial production and employment. The Markov chain approachis a parsimonious approach that allows us to examine the cyclical dynamics of differenteconomic time series using limited judgment on the issue. Time homogeneity and timedependence tests are implemented to determine the stationarity and dependence propertiesof the series. Univariate processes for industrial production and employment growth areestimated individually and a composite indicator that combines information on these seriesis also constructed. Tests of equality of the estimated Markov chains across countries arealso implemented to identify similarities and differences in the cyclical dynamics of therelevant series.

Keywords: Markov chain models, economic indicators, cross-country analysisJEL Codes: C22, E32, E37.

∗We are grateful to Peter Benczur for providing us with the multi-country data set that formed the basis oftheir paper “Business Cycles around the Globe”.

1

1 Introduction

Modeling business cycles dynamics using Markov processes and Markov chains has an im-portant tradition. In early work, Neftci (1984) investigated the issue of asymmetry betweenexpansions and contractions of a business cycle using a framework of discrete Markov chains.Neftci (1984) argued that the behavior of unemployment rate in the United States can be char-acterized by sudden jumps and slower drops. Hamilton (1989) proposed a simple nonlinearframework for modeling economic time series with a permanent component which follows aMarkov switching process as an alternative to a stationary linear autoregressive model. In hisframework, recessions are due to permanent negative shocks. Another type of business cycleasymmetry is due to Kim and Nelson (1999). This is known as the “plucking model” of busi-ness cycles. Here recessions occur as temporary deviations from the long-run level of GDP asoccasional “plucks” whereas expansions reflect permanent shocks. Kim and Piger (2002) pro-pose a framework which allows for infrequent asymmetric transitory shocks which come froma Markov process as well as continuous transitory symmetric shocks. Markov chain-based ap-proaches have also been used in the labor economics literature to model labor market dynamics.Flinn and Heckman (1982) use Markov chain methods to develop a structural model of labormarket search and to estimate its parameters. Eckstein and van den Berg (2007) present anup-to-date survey of empirical labor market search. In a developing economy context, Alvarez,Ciocchini and Konwar (2008) use discrete Markov chain methods to characterize the dynamicsof Argentinian labor markets in a period that also encompasses the Argentinian crises of 1995and 1998-2002.

In this paper, we characterize the business cycle as a recurring Markov chain for a broad setof developed and developing countries. Our objective is to understand differences in cyclicalphenomena across a broad range of countries based on the behavior of two key economic timesseries – industrial production and employment. The Markov chain approach is a parsimoniousapproach that does not require an extensive set of assumptions regarding the distribution,homoscedasticity, serial correlation properties of the time series under consideration. In aseries of papers, Harding and Pagan (2002a,b) have argued that the approach based on theMarkov switching model may produce different business cycle characteristics relative to linearmodels depending on assumed features such as conditional heteroscedasticity, persistence, andnon-normality of the process. More importantly, the Markov chain approach used in thispaper allows a test of the time-dependency and time-homogeneity of the estimated Markovchains, a feature which is typically absent from applications of the Markov-switching model.One disadvantage of the Markov chain approach, however, is that some of the details of theunderlying stochastic process are lost when a continuous state space of a given time seriesis aggregated into a discrete one. Tan and Yilmaz (2002) implemented Markov chain-basedtests of time dependence and time homogeneity in the context of tests of market efficiency andexamined the efficacy of the Markov chain approach using simulation methods. In this study,we extend their approach to the analysis of cyclical phenomena in a cross-country basis. Ourapproach is also related the work of Neftci (1984), who used a discrete Markov chain approachto model the behavior of US unemployment over the postwar period.

Burns and Mitchell (1946) were the first investigators who set out the nonparametric meth-ods to determine the characteristics of cycles in economic time series. They laid the foundationsof documenting recurrent cycles of quantities and prices. Nonparametric approaches extractinformation about the evolution of an economic time series directly from the observation of

2

the historical data. Thus, this approach works even when reliable information on the para-metric function is not provided. The possibility that the behavior of the economic time seriesmay have changed in the past is also taken into consideration, and predictions are made bytaking into account such changes (see Andersson, Bock and Frisen, 2004). The nonparametricapproach which is used by NBER in order to detect turning points of business cycles is derivedfrom Bry and Boschan’s (1971) influential work where no formal statistical model is used dur-ing the process. Bry and Boschan’s approach is a nonparametric procedure which is applied toa single monthly time series adjusted for seasonality. As we discussed above, there are numer-ous parametric approaches to modeling business cycles. Implementation of parametric modelssuch as the Markov-switching model involve judgments about how many states are includedin the model and whether the transition probabilities are constant during the observed timeinterval. This means that the time-homogeneity of observed series is not properly tested. Onthe other hand, the simple Markov chain approach does not involve such assumptions aboutthe stationarity of the time series in consideration.

In this paper, we implement formal tests of time-homogeneity of the series to determineif the transition probabilities between the states of the Markov model are invariant over timeor not. The systematic time-dependence and time-homogeneity testing procedure thus en-ables us to make realistic inferences about the cyclical dynamics of economic time series usinglimited judgment on the issue. Our study permits the detection of breaks in the estimatedtransition probabilities. This approach leads to using different transition probabilities for dif-ferent time periods depending on the determined breaks in the period under investigation.As Filardo (1994) indicates, a model with time-varying transition probabilities can character-ize the dynamics of business and growth cycles better than the fixed transition probabilityapproach and standard linear time series model. In recent years, a number of studies haveinvestigated the impact of various institutional factors on business cycle characteristics. See,for example, Canova, Cicarrelli and Ortega (2009) or De Pace (2010). In our study, we usedinformation about such underlying institutional, political or policy changes when testing fortime-homogeneity of the economic time series. Hence, our approach relates such factors topotential nonlinearities in the underlying series.

Another contribution of our study is that we can use Markov chain-based tests to identifysimilarities and differences in the cyclical dynamics of the relevant series. By comparing theestimated transition probabilities of two countries by using a Markov chain-based test, weformally test whether the cyclical dynamics of one country can be differentiated from anotherone. Furthermore, we use a first passage time analysis to determine the mean and the coefficientof variation of the first passage times between the states above and below the trend. Thesefirst passage times also give additional information regarding the similarities and differencesbetween the cyclical dynamics of different countries.

The rest of this paper is organized as follows. Section 2 describes the methodology whileSection 3 discusses the notion of economic indicators as well as the data used in this study.Section 4 describes how to implement tests of time homogeneity and time dependence whileSection 5 describes the results of implementing such tests. Section 6 implements tests ofthe statistical difference of the estimated Markov chains between the different countries whileSection 7 examines the expected first passage times between the different states. Section 8shows how the analysis can be extended to derive composite indicators. Section 9 concludes.

3

2 Methodology

In this study, we propose and use a Markov chain-based methodology for investigating thecyclical behavior of key economic aggregates. More specifically, we view a business cycleas a recurring Markov chain. The length of time this process is expected to spend in eachstate before switching to the other state gives statistical information regarding this alternatingprocess.

Formally, we view a given economic time series y(t) as a discrete parameter, continuous statespace stochastic process {y(t), t = 1, 2, . . .}. In order to utilize the Markov chain methodology,we aggregate the continuous state space of the time series into a discrete state space witha finite number of states. That is, the process {y(t), t = 1, 2, . . .} is mapped into a discreteparameter, discrete state space stochastic process defined as {Xt, t = 1, 2, . . .} on the statespace S.

The aggregation of the state space and the definition of the state space depend on thestatistical properties of the time series under investigation. To analyze cyclical dynamics ofeconomic time series (e.g. capacity utilization rates, industrial production indices, stock prices)as a Markov chain, it is sufficient to focus on the direction of movements of the time serieswhich indicate whether the consecutive states show an increase or decrease over time. Thisapproach has been used extensively in the literature. One can use more states in S to includemore information on y(t) in Xt to study not only the direction of change but also the magnitudeof change. However, the increased number of states requires a greater probability transitionmatrix to estimate and reduces the power of the tests power when the number of observationsis limited. It is shown that analyzing a time series as a two-state recurring Markov chain issufficient to analyze its cyclical dynamics (Tan and Yilmaz 2002).

In this study, the continuous state space of a stationary economic time series is mappedinto a discrete state space S = {U,D} where U corresponds to an upward movement of y(t)at time t, D corresponds to a downward movement of y(t) with respect to its average duringthe full period [0, T ], y = 1/(T + 1)

∑Tt=0 y(t), i.e.,

Xt =

{U if y(t) ≥ yD if y)t) < y.

In economic time series which exhibit a trend over the sample period, the movements in theseries are defined relative to this trend.

Our methodology starts with determining the time-dependency and time-homogeneityproperties of the two-state Markov chain obtained from the economic time series that isbeing investigated. The first step of our methodology tests whether the time series underinvestigation can be represented as a time-homogeneous Markov chain of a determined order.The outcome of this step is a time-homogeneous probability transition matrix that gives theestimated transition probabilities between the states depending on the determined order oftime dependency. Alternatively, we can conclude that the time series cannot be representedas a time-homogeneous time series in the time period being investigated. In this case, wecan continue with searching another starting point for the time series that may yield a time-homogeneous Markov chain representation.

Once we ensure the time homogeneity and determine the order of time dependency, we usethe estimated probability matrix to analyze the statistical properties of the time series. We

4

also use the estimated probability matrices of two countries to test whether the Markov chainsof these countries are statistically different. Furthermore, we use a first-passage time analysisto determine the expected times the process spends in state U until it switches to state D andthe expected time it spends in state D until it switches to state U . This analysis also gives usinformation about the distribution of the switching times and thus answers questions on theprobability of observing a transition into another state within a given time period.

Unlike other parametric approaches, this methodology allows us to directly test the time-dependency and homogeneity properties of the underlying time series without making distri-butional assumptions.

Our discussion follows from Tan and Yilmaz (2002). For a more detailed discussion ofthe procedures, the reader is referred to Anderson and Goodman (1957) and Kemeny andSnell (1976). In the next section, first the methodology to test for time-dependency and time-homogeneity given in (Tan and Yilmaz 2002) is summarized. Then the methodology to testthe statistical difference between two time series, and also the methodology to analyze thepassage times between the up and the down states are presented.

2.1 Definitions

A Markov chain of order u is completely characterized with its state transition matrix P (t) ={pi,j(t)} where

pi,j(t) = P (Xt+1 = j|Xt = i1, . . . , Xt−u+1 = iu),

i = (i1, . . . , iu)′ ∈ Su, j ∈ S, t = u− 1, u, u + 1, . . . (1)

In this representation the state i includes more than one state if the order of time dependencyis greater than one. For example, for a second order Markov chain defined on the state space{U,D}; i ∈ {UU, UD, DU, DD} and j ∈ {U,D}.

The above definition shows that whenever the stochastic process is in state i, there is aprobability pi,j(t) that it will be in state j at time t + 1. When the transition probabilitiesbetween states do not vary over time, then the underlying Markov chain is time homogeneous.In this case, when in state i at time t, the probability that the process will next make atransition into state j is independent of time t. This implies, for a time homogeneous Markovchain pi,j(t) = pi,j and therefore P (t) = P .

Consequently, for a given sequence {Xt, t = 0.1, 2, . . .} is an independent process then theprobability law of the process is given by:

P (Xt = j|Xt−1 = i1, . . . , X0 = it) = P (Xt = j).

Similarly, for a first-order Markov chain,

P (Xt = j|Xt−1 = i1, . . . , X0 = it) = P (Xt = j|Xt−1 = i1);

and for a second-order Markov chain,

P (Xt = j|Xt−1 = i1, . . . , X0 = it) = P (Xt = j|Xt−1 = i1, Xt−2 = i2).

5

2.2 Estimation of State Transition Probabilities

For a time-homogeneous Markov chain order u, the transition probabilities can be estimated di-rectly from the observed transitions. The maximum likelihood estimates of the state transitionprobabilities are given as

pi,j =ni,j∑i ni,j

, i ∈ Su, j ∈ S, (2)

where ni,j represents the total number of observed transitions from state i to j during thegiven time period (Anderson and Goodman 1957). Once the transition probabilities have beenestimated, they can be used to construct tests of time dependence and time homogeneity of theMarkov chain in question. We present the relevant tests in Section 4. In that section, we alsoshow such tests can be extended to test for the equality of the transition probabilities of twodifferent Markov chains. Finally, using the results of Appendix A, we calculate the expectedfirst passage times for the different economic indicators considered in this study.

3 Economic indicators

In this study, we analyze the behavior of industrial production and employment growth aseconomic indicators which provide information about the underlying trends of the economy.Economic indicators can be classified as leading or lagging. As Lahiri and Moore (1992)argue, it may be useful to identify series as leading indicators since market-oriented economiesexperience business cycles where repetitive sequences are observed. These sequences not onlyunderlie the generation of business cycles but also constitute the most useful data to forecastthe turning points of economic activity.

The industrial production index is an economic indicator which measures the real growthrate in industrial production of a nation. It represents the industrial capacity measure and theavailability of resources among factories, utilities and mines. It is well known that the largestcomponent of industrial output is generated by manufacturing and manufacturing itself isconsidered to be one of the major cyclical sectors of the economy. Thus, growth in industrialproduction plays a key role in defining turning points of a business cycle. Unemployment datais generally considered as a lagging indicator by many economists, as it is destined to increaseafter the official end of a recession in the economy and displays a sharp decrease after the peakof the business cycle. On the other hand, historically, the unemployment rate has peaked moreoften fairly close to the end of recessions. Hence, there are those who argue that employmentdata should be considered more than a lagging indicator.

Existing business cycle studies have examined the behavior of industrial production asmuch as they have concentrated on the behavior of aggregate real GDP. Artis, Kontolemisand Osborne (1997) and Artis, Krolzig and Toro (2004) use industrial production data toexamine business cycles in G7 and the Euro area, respectively, using both parametric andnonparametric approaches. The cyclical behavior of aggregate employment has been one ofthe key issues around which the debate about the efficacy of the Real Business Cycle model inreplicating aggregate fluctuations has evolved. (See, for example Hodrick and Prescott, 1997,and Gali, 1999.) In his influential study, Neftci (1984) argues that economic time series suchas the unemployment rate are related to the production side of the economy. Hence, they

6

give a better indication of business cycles than other variables that are not directly linked realeconomic decisions.

In this paper, we analyze the cyclical dynamics of industrial production and employment ofa broad set of countries playing key roles in the global economy. The full set of countries usedin our study is similar to the set considered by Altug and Bildirici (2010), and it comprises aset of developed countries including Australia, Canada, the UK, the US and Japan plus theEU countries of Finland, France, Germany, Italy, the Netherlands and Spain as well as a setof developing countries including the East Asian countries of Malaysia, Philippines, and S.Korea, the Latin American countries of Argentina, Chile, and Mexico and a set of countriestypically considered among the emerging economies including China, S. Africa and Turkey.Data on the industrial production index is typically available from the International FinancialStatistics (IFS) database of the IMF. Data on aggregate employment can be obtained fromthe International Labor Office (ILO), Eurostat or Bank of International Settlements (BIS).

Let yi,t = ln(Yi,t) where Yi,t denotes the industrial production index (or total employment)of country i in quarter t. We take the annual quarter-to-quarter growth rate of GDP forcountry i as ∆yi,t = ln(Yi,t) − ln(Yi,t−4). For seasonally unadjusted data, this transformationtends to eliminate any seasonal effects that might exist at the quarterly frequency. In somecases the underlying growth series may exhibit a trend – typically a negative trend – over thesample period. In this case, we calibrate the Markov chain relative to this time-varying trend,and not the simple sample average described in Section 2.1.

4 Tests of time homogeneity and time dependence

In this section we describe how to test for time dependence and time homogeneity of theestimated Markov chains for each country individually. These tests allow us to determine theorder of the Markov chain and also whether it follows a stationary process.

4.1 Testing for time dependence

In order to test time dependence, we first assume that the Markov Chain is time homogeneousin the time period that is being investigated.

Let P = {pi,j} denote the time homogeneous state transition matrix of Markov chainof order u and Q = {qi,j} denote the transition matrix for order v. In order to test the nullhypothesis that the Markov chain is of order u versus order v such that v > u, an asymptoticallyequivalent test statistic for the likelihood ratio test statistic is given in (Tan and Yilmaz 2002)as

−2 ln(Λ) = 2∑i,j

ni,j [ln(qi,j)− ln(qi,j)] , i ∈ Sv, j ∈ S, (3)

with

Q = {qi,j} =[PT, PT, . . . , PT

]︸ ︷︷ ︸

2v−u

T

where AT denotes the transpose of matrix A.

7

This test statistic has a χ2 asymptotic distribution with 2v − 2u degrees of freedom. Theorder-test procedure starts with testing the null hypothesis that the given time series is anindependent process (with u = 0) versus the alternative hypothesis that the time series is aMarkov chain of first order (with v = u + 1), and if it is rejected continues by increasing u byone and applying the same test with order u versus u + 1. This procedure lasts until the nullhypothesis is not rejected.

Since it is assumed that the Markov chain is time homogeneous to perform this task, thisassumptions must be tested to finalize the time-dependency test.

4.2 Testing for time homogeneity

In order to test a time series for time homogeneity, we divide observations on {Xt, t =0, 1, 2, . . .} into K different equal sub-intervals. This test involves testing whether the esti-mated transition probabilities of each subinterval are statistically different from the transitionprobabilities estimated for the full time period.

The state transition probability of a uth order Markov chain corresponding to period k, k =1, 2, , K is given by

pi,j(k) = P (Xt = j|Xt−1 = i1, . . . , Xt−u = iu),

i = (1i, . . . , iu) ∈ Su, j ∈ S, t ∈ [(k − 1)∆, k∆], (4)

where ∆ = b(T + 1)/Kc. We would like to test the null hypothesis that the transition proba-bilities for each subinterval P (k) = {pi,j(k)} are not statistically different from the transitionprobabilities determined for the whole period P = {pi,j} versus the alternative hypothesis thatthey are different. To conduct the hypothesis test, an asymptotically equivalent test statisticfor the likelihood ratio test statistic is given in (Tan and Yilmaz, 2002) as:

−2 ln(Λ) = 2∑k

∑i,j

ni,j(k) [ln(pi,j)(k)− ln(pi,j)] ,

i ∈ Su, j ∈ S, k = 1, 2, . . . ,K (5)

where ni,j(k) is the number of observed transitions from state i to state j for subinterval k.This test statistic has a ξ2 asymptotic distribution with 2(K − 1) degrees of freedom.

In case the null hypothesis is not rejected, one can admit the time series analyzed is timehomogeneous. Otherwise, the time dependence test cannot be done by using a single probabilitytransition matrix estimated by observation of the empirical data.

5 Results

Tables 1 and 2 provide the estimated transition probabilities for the behavior of industrialproduction (IP) growth and employment growth for the entire sample of countries. The resultsof tests for time homogeneity and time dependence are also reported in these tables. Column1 shows the beginning year for which time homogeneity of the series can be established whileColumn 2 shows the order of the estimated Markov chain. In our analysis, we typically reportthe time series properties of the economic indicators in the period after a break is detected, ifsuch a break exists. By focusing on the most recent period for which time-homogeneity can

8

be established, we also ensure that the estimated Markov models in this paper have predictivepower for future developments in the economy.

5.1 The developed countries

We examine cyclical phenomena for the developed countries using country groupings suggestedby Altug and Bildirici (2010). Thus, one group of developed countries is termed the Anglophonecountries plus Japan while the second group comprises a set of EU countries. Equivalently, thedeveloped countries that we study may be examined in terms of the G7 countries consisting ofthe US, Japan, Germany, France, the UK, Italy and Canada plus a set of smaller industrializedsuch as the Finland, Netherlands, Spain and Sweden.

Beginning with the US, we find that both IP and employment growth both have negativetrends over the sample period. Hence, the Markov chains for these variables are calibratedrelative to their individual-specific trends. Tests of time homogeneity and time dependenceshow that time-homogeneous Markov chains of order one can be used to represent changesin IP and employment across the sample period 1960-2008 for the US.1 We also find that IPand employment growth follow time-homogeneous processes for Australia, Canada, and theUK over the available sample periods, and that IP and employment growth follow first-orderprocesses for Australia, Canada, and the US. This is also the case for employment growth inthe UK. However, we find that IP growth in the UK follows a second-order process. Since thetime-dependence properties are obtained as a result of formal testing, this result suggests asignificant difference in the cyclical dynamics of the UK relative to the remaining Anglophonecountries. There are also some salient differences in the expected first passage times acrosscountries for both IP and employment growth. Specifically, the expected first passage times forUS IP growth tend to be longer than those for the other Anglophone countries. More tellingly,though, we find that employment growth in the UK is a much more persistent process relativeto those for the other Anglophone countries and indeed relative to those for all of the developedcountries with the exception of Spain that we discuss below. In the next section, we provideresults of formal tests to determine whether such differences are statistically significant or not.

Turning to EU countries, Markov chain-based time-homogeneity and time-dependence testsimply that IP growth processes for Germany, France, Italy, Finland and Spain follow ho-mogeneous patterns across the available sample periods. However, we can estimate a time-homogeneous process for IP in the Netherlands only since 1963. Furthermore, unlike the pro-cesses in Germany, France, Italy, Finland and Spain, IP growth follows a second-order processin the Netherlands. Second, employment growth shows homogeneous behavior in Germany,France, the Netherlands, Finland, and Spain. However, the Markov chain for employmentgrowth in Finland is of second-order, unlike the case for the other developed countries.

There are also a set of developed counties for which the Markov chain-based time homo-geneity tests are rejected. A notable example in this regard is Japan. Tables 1 and 2 show

1It is interesting to compare this result with Neftci’s (1984) results, who found that movements in thequarterly unemployment rate follow a second-order Markov chain. During the application, Neftci also supposesthat the unemployment rate is a stationary series. On the other hand, Neftci does not use any time homogeneityor time dependence tests in order to justify these assumptions. Using quarterly data on unemployment ratesfor the U.S. over the period 1948-2008, we found that this series is a homogeneous stochastic process following afirst-order Markov chain. Our results verify the validity of Neftci’s results and they also show that there existsno discernible break in the behavior series such as IP and employment growth or the unemployment rate.

9

that both IP and employment growth follow non-homogeneous processes over the sample pe-riod. We find that 1993 appears as a natural breakpoint for the Japanese economy after whichtime-homogeneity of both IP and employment growth can be established. As is well known,the Japanese economy entered a long period of recession and stagnation in the early 1990’s.The Economic Cycle Research Institute (ECRI) gives the date of the first Japanese recessionin the 1990’s as 1992:2. The “lost decade” in Japan has been studied extensively. Meltzer(2001) claims that the maintained growth rate of Japan slowed and Japan’s cost of produc-tion rose relative to U.S production costs in the 1990’s. “To restore 1980’s growth requiredeither increased productivity growth, real currency depreciation, or deflation. Japan’s policymakers, by choice or accident, chose deflation instead of currency depreciation” (see Meltzer,2001). Even industries such as automobiles and electronics that had experienced extraordinarygrowth in 1980’s entered a recessionary phase in the early 1990’s. This continued until thezero or negative growth of the real monetary base ended in 1993, suggesting that 1993 servesas a breakpoint for the behavior of the Japanese economy.

We also find that employment growth for Italy is not time-homogeneous. 1993 emergesas a breakpoint in this case as well. Tiraboschi and Del Conte (2004) argue that the 23 July1993 agreement signed by the socialist parties and the Italian Government was a turning pointin Italian industrial relations. This agreement was based on the will to bring pay settlementsinto line with rigorous incomes policy in order to combat inflation, which was considered as abase step for entry into the EU Economic and Monetary Union (EMU). Following this period,a combination of factors, one being the tax burden on employment, caused the unemploymentrate to rise to 11.3% and led to an inflation rate 5%, which was higher than that of Italy’smain trading partners. In the middle of 1990’s, the unemployment rate started to decreaseagain due to the 28 November 1996 legislations, which were designed to promote access toemployment.

5.2 Developing countries

The developing countries tend to have both different cyclical dynamics relative to the devel-oped economies and also to display much less stability. Furthermore, we show that there aresignificant differences among these countries, even ones with similar historical or geographicalcharacteristics.

The East Asian countries have been known for their remarkable economic success. Beforethe 1960’s, Korea had been one of the poorest economies. Yet Korea has been one of theworld’s fastest growing economies since the early 1960’s through the late 1990’s, and it isnow classified as a high-income economy by the World Bank and an advanced economy bythe IMF. According to the data collected in 1980-2008, we do not observe a breakpoint inindustrial output or employment performance of Korea.

Before the 1997 Asian financial crisis, Malaysia had been known as a popular investmentdestination which caused expectations that economic growth would continue. However, in July1997, the currency of Malaysia - the ringgit - suffered a speculative attack. In 1998, real outputgrowth fell and Malaysia entered into its first recession for a long time period. From Table1, we observe that IP growth in Malaysia does not follow a time-homogeneous over the entiresample beginning in 1985, and that 1998 serves as the breakpoint in the time-homogeneitytests. However, the estimated process for IP growth since 1998 is of order one, as is the casefor S. Korea and has similar expected first passage times. By contrast, employment growth

10

since 1997 for Malaysia can be represented as an i.i.d process with very short expected firstpassage times between the two states.

Unlike many of its neighbors, Philippines had not experienced a long-term rapid growthsince the 1970’s due to its weak political and institutional foundations. Even in the 1990’scorresponding to the peak years of growth for the Asian countries, growth in the Philippinesdid not exceed 6%. As a consequence, IP growth in the Philippines is generally low and stable,and time-homogeneous first-order Markov processes suffice to capture the behavior of IP andemployment growth over the observed sample periods.

In contrast to the East Asian economies, the Latin American countries exhibit far greaterheterogeneity. From being a wealthy economy with rich natural resources and an export-oriented agricultural sector with a relatively diversified industrial base, Argentina entered along period of decline and suffered from a series of economic crises during 1981-2002. Argentinaentered 2001 with an economy already mired in a long recession period, partly attributableto the contagion effects of Russia’s debt default in August 1998. This caused investors toavoid emerging markets and also raised the cost of Argentina’s foreign borrowing. By 2002,the economy suffered its sharpest decline since 1930: Argentina had defaulted on its debt. Asa result, we find that both IP and employment growth are time-homogeneous processes oversamples that begin in 1997 or 1998. We also find that the process for employment growthin Argentina is highly persistent, reflecting the dynamics of the crises that this country hasendured over the sample period.

For the Mexican economy, the signing of the North American Free Trade Agreement(NAFTA) in 1994 between Canada, the US and Mexico constitutes an important turningpoint. The increase in regional integration among NAFTA partners also affected business cy-cles in Mexico and led to a significant increase in the co-movement of business cycles withinthe NAFTA region (Kose, Meredith and Towe, 2004). For this reason, when analyzing thebehavior of IP growth, 1994 is considered a breakpoint for the Mexico economy. From Table1, we observe that IP index growth of Mexico can be represented with a first-order Markovprocess after 1994. By contrast, we observe that employment growth for Mexico can only berepresented with a time-homogeneous process since 2000.

Like most of other countries in Latin America, Chile had experienced economic crisis inthe early 1980’s which caused sharp decreases in industrial output. On the other hand, unlikeMexico, Chile economy succeeded in recovering rapidly and grew consistently during 1980’s.This success may be due to the early reforms undertaken in the 1970’s which set the stage forthe successful performance of Chile in the 1980’s (Bergoeing, Kehoe and Soto, 2001). Thesefacts are mirrored in the behavior of IP growth in Chile, which can be represented as a time-homogeneous Markov process over the available sample period stretching back to 1960. Bycontrast, we find that employment growth can only be characterized as a time-homogeneousprocess since 1999.

In the remainder of this section, we consider three other emerging market economies. Fol-lowing Mao’s death, gradual market reforms were initiated and the free-market system began totake hold in China. Today, China is one of the fastest-growing and most important economiesin the world, and it has been undergoing a process of very rapid industrialization. In contrastto the process of “de-industrialization” in the US, both IP and employment growth have sig-nificant positive trends in China over the respective sample periods.2 We find that both IP

2Bronfenbrenner and Luce (2004) provide evidence regarding the impact of a production shift on jobs from

11

and employment growth can be represented by homogeneous first-order Markov processes afteraccounting for the positive trends in both of these series over the relevant sample periods.

The South African economy was able to display average growth rates of 2.1% and 1.4%in the 1980’s and 1990’s, respectively. However, real GDP growth was more volatile duringthe 1980’s than in the 1990’s (Hodge, 2009; Altug and Bildirici, 2010). Our analysis revealeda breakpoint of 1983 for IP growth. One criterion for choosing this year as a breakpoint isthat employment growth was 3.7% in 1982, the highest employment growth rate until 2004.However, our analysis revealed no breakpoint for employment growth but this may be due tothe shorter sample for this series.3

Turkey suffered from two major economic crises in recent years, one of which occurredin 1994 and the other in 2001. We observe a large decline in IP growth in 1994, which isdue to the 1994 currency crisis. This crisis caused the highest level of annual output loss inthe history of the Turkish Republic. On the other hand, the 2001 crises had deeper effectson Turkish economy. During 2001, GNP fell by 5.7% in real terms, consumer price inflationincreased to 54.9% and the currency lost 51% of its value against the major foreign monies.The rate of unemployment rose up to 10% and real wages were reduced by 20% upon theimpact of 2001 crisis (Yeldan, 2008). For IP growth, the breakpoint occurs in 2002 while foremployment growth, it occurs earlier in 2000. Beginning with these years, we observe that theestimated Markov processes for both IP and employment growth are i.i.d processes with veryshort expected passage times between the two states, reflecting the lack of any major crises inthis period except the 2008 financial crisis.4

Summarizing, we find that there is greater evidence against time-homogeneity in the es-timated Markov processes for the developing countries relative to developed ones. With theexception of the fast-growing East Asian economies, almost all of the developing countriesexhibit some form of nonstationarity in the processes describing IP and employment growth.This no doubt reflects the experience of major crises as well as institutional and policy changesthat such economies have undergone. This finding is also evident in the nature of the estimatedprocesses over periods for which time-homogeneity can be established.

6 Testing for statistical difference between the cyclical dynam-ics of two countries

Our analysis in the previous section shows some noteworthy differences in the stochastic pro-cesses describing the cyclical dynamics of IP and employment growth for individual countries.

the US and Europe to countries such as China, India, other Asian countries, Mexico and so on.3Our analysis also did not reveal a breakpoint in 1994 associated with the ending of apartheid in 1994.

However, the lower and less volatile growth may be attributed partly to this phenomenon as well as the lengthyprocess of adjustment in employment growth.

4As a point of comparison, we can also examine the behavior of the estimated Markov process for IP growthin the period between 1980-2001 for Turkey. This is a first-order Markov process with the following transitionprobability matrix:

P =

[0.6957 0.30340.3514 0.6486

]with E(TU,D) = 3.28 and E(TD,U ) = 2.84.

These are similar to the properties of the estimated Markov chains for countries such as China or S. Korea.Hence, we find that the cyclical properties of IP are not out of line with experience of other developing economies.

12

These differences are reflected in the persistence properties of the estimated Markov chains. Wenow test formally to determine whether such differences are statistically significant. This testinvolves testing whether the estimated transition probabilities of each country are statisticallydifferent from the transition probabilities estimated by combining the time series. That is, ifthe cyclical dynamics of two countries cannot be distinguished from each other statistically,then the transition probabilities of these two countries are estimated by using the combinedtime series of both countries.

We assume that the estimated order of time dependency for both countries is the same anddenoted by u. Note that if these countries have different order of time dependency, we canstate automatically that their cyclical dynamics are statistically different.

We would like to test the null hypothesis that the transition probabilities for countries A andB, P (A) = {pi,j(A)} and P (B) = {pi,j(B)} are not statistically different from the transitionprobabilities determined for both countries P = {pi,j} versus the alternative hypothesis thatthey are different. By following the approach for the time-homogeneity test, an asymptoticallyequivalent test statistic for the likelihood ratio test statistic can be given as

−2 ln(Λ) = 2∑

c

∑i,j

ni,j(c) [ln(pi,j)(c)− ln(pi,j)] , i ∈ Su, j ∈ S, c ∈ {A,B}. (6)

where ni,j(c) is the number of observed transitions from state i to state j for country c. Thistest statistic has a ξ2 asymptotic distribution with 2 degrees of freedom.

In case the null hypothesis is not rejected, one can state that the transition probabilities ofthese two countries are not statistically different. Otherwise, the transition probabilities, andtherefore the cyclical behavior, of these two countries can be considered statistically different.Tables 3 and 4 report the p-values, or the probability that the value of likelihood ratio statisticis less than its sample counterpart, for IP and employment growth, respectively.

6.1 Test results for IP and employment growth

From Table 1, we observe that the estimated Markov chain for Turkey is i.i.d and those forthe Netherlands and the UK are of order two. A priori this is evidence indicating differencesin the cyclical dynamics of IP growth for Turkey vis a vis all of the other countries in Table2 as well as those for the Netherlands and the UK vis a vis the remaining countries. Table1 shows that the process for IP growth estimated over the period since 2002 for Turkey hasvery short expected first passage times. While the second-order processes for IP growth for theNetherlands and the UK differs from those for the remaining countries, the p-value for theirequivalence is 0.1616, indicating that these processes cannot be differentiated from each other.In Table 3, we report the p-values pertaining to those countries whose IP growth follows a first-order process. Here we observe that among the developed countries Spain stands out in termsof the properties of its IP growth process. We can reject at the 10% level that IP growth inSpain follows the same process as those for other developed countries such as Australia, Japan,Finland, and France as well as for Chile, S. Korea, the Philippines, and China. Table 1 showsthat the reason for this finding lies in the sluggish behavior of Spanish IP growth, especiallyin the “Down” state. We argue below that this finding may be related to the behavior ofemployment growth in Spain.

We do observe a group of East Asian countries for which the cyclical dynamics of IPgrowth appears to differ from other developed and developing countries - namely, China, the

13

Philippines and S. Korea - at the same time that it exhibits similar behavior across thesecountries. Table 3 shows that the process for IP growth for S. Korea differs significantly fromthat for Canada, the US, Germany, Spain, Argentina, Chile, and S. Africa, the process forChina differs from that for Canada, the US, Spain, Chile, and Argentina, and the processfor the Philippines differs from that for Canada, the US, Spain and Chile. From Table 1, weobserve that IP growth for China, S. Korea and the Philippines appears to spend relativelyshort periods either above or below expected IP growth. This contrasts with a country suchas the US whose expected first passage time from above trend to below trend IP growth isamong the longest in the sample or with countries such as Spain or Argentina which exhibithighly persistent IP growth. Conversely, we cannot reject the hypothesis that the processesdescribing IP growth for many of the EU countries do not differ from each other or from otherdeveloped and developing countries.

Next, we turn to tests of the equivalence of the processes for employment growth acrossthe different countries. First, from Table 2, we observe that the expected first passage timesfor the employment processes tend to be longer than those for IP growth for most of the coun-tries in our sample. Second, we find greater heterogeneity in the estimated Markov processesfor employment growth. For one, Malaysia, Mexico and Turkey possess i.i.d. processes foremployment growth, reflecting the experience of crises and hence, the shorter horizon overwhich stationary employment processes can be estimated. Second, while the process for em-ployment growth for Finland is stationary over the available sample periods, its behavior canbe represented by a second-order process for this country. This finding constitutes evidence forsignificant differences in employment growth for countries with estimated processes followingi.i.d or order two processes relative to those following order one processes. As before, we cantest for the equivalence of the processes among the first country group. The results of thetests of the equivalence of the employment processes for Malaysia, Mexico, and Turkey do notindicate any evidence of significant differences.5

Table 4 reports the test results for the remaining countries whose employment processesare of order one. Here we observe that the employment growth processes for Spain and theUK are estimated to be significantly different from most of the other developed and developingcountries for which a relevant comparison can be made. Specifically, out of the 15 countriesreported in Table 4 with first-order employment growth processes, the process for Spanishemployment growth differs significantly from 11 of these processes while UK employment differsfrom 8 of them. The reason for these differences stems from the highly persistent nature of bothSpanish and UK employment growth. The persistence of the UK unemployment rate is wellnoted.6 To understand the reasons for this phenomenon, we observe that the annual growthrate for the UK economy in the 1960-1973 period was far below the rates of other Europeancountries like France, West Germany and Italy and remained low after the 1973 oil shock. Theelection of Margaret Thatcher in 1979 ushered in a new period of neo-liberal economic policies,which initially led to mass unemployment. Unemployment rose again as a result of the ERMcrisis of 1992. However, during the ten years of Tony Blair’s rule since 1997, inflation, interestrates and unemployment all remained relatively low until the 2008-2009 recession due to theglobal financial crisis (see Tang, 2008).

5The p-values for the test between the employment processes for Malaysia and Mexico is 0.495, for Malaysiaand Turkey is 0.8851, and for Mexico and Turkey is 0.8090.

6See, for example, Arulampalam, Booth, and Taylor (1998), who study this phenomenon using individual-specific data.

14

The experience of Spain also reflects some idiosyncratic features. Perhaps Spain is theonly country in our sample that can be considered in the EU “periphery” (see, for example,Giannone, Lenza and Reichlin, 2008). Despite showing impressive gains during the processof European Union integration, the Spanish economy has also had the highest unemploymentrates in the EU (see Blanchard and Jimeno, 1995). The persistence of Spanish unemploymenthas been an oft-mentioned phenomenon.Alana and del Bario (2006) corroborate this findingusing regional unemployment data and find that persistence of unemployment is greater inthe most industrialized regions in Spain.7 They conjecture that the low rate of interregionalmigration may be as important in explaining such persistence as the institutional features ofSpanish labor markets.8

The results of Table 4 also provide some noteworthy conclusions regarding the processesfor employment growth in developing countries. Here we find that the employment growthprocesses for the Philippines, Chile and China are significantly different from those of developedor other developing economies. Countries such as Chile and the Philippines display shortexpected first passage times, in contrast to other developed or developing economies. Bycontrast, employment growth in China tends to remain below trend longer than for manyother economies.

7 Expected first passage times and their variability

The first passage time to switch form from up states to down states and from down statesto up states gives information related to the cyclical dynamics of economic time series. Byusing the first passage analysis presented in Appendix A, Figures 1 and 2 display the expectedvalue of the first passage times between the different states and their coefficient of variation(CV) for IP and employment growth of each country analyzed in this study, respectively.One way to interpret such patterns is to use notions of proximity. Geographical proximitysuggests that despite the increasing mobility of commodities, ideas, and people, the diffusionof economic activity is very unequal and remains agglomerated in a limited number of spatialentities (Combes, Mayer and Thisse, 2008). Organizational proximity denotes the interactionability among members of an organization (Torre and Rallet, 2004). Technological proximityand global networks, on the other hand, refer to the shared technological experiences andknowledge bases (Oerlemans and Knoben, 2006).

Figures 1 and show that observations on expected passage times for the different countriesgenerally cluster together. However, this clustering is more dense for IP growth than employ-ment growth. For European countries such as France, Germany and Italy, we see the expectedpassage times between the different states of IP growth are very close. Employment growth

7As we noted above, this finding may also explain the persistence of IP growth in Spain.8The greater persistence or hysteresis in employment patterns that many EU economies have displayed es-

pecially since the oil shocks of 1970’s and 1980’s was noted Blanchard and Summers (1989), who define thissituation as one in which the equilibrium unemployment rate depends on the history of the actual unemploymentrate or equivalently, that there is path-dependence in the underlying equilibrium of the economy. The expla-nations that have typically been given for this phenomenon focus on alternative labor market institutions andpractices. Ball (2009) re-visits the hysteresis hypotheses and presents evidence for it using data on twenty OECDcountries since the 1980’s. He argues that the evidence regarding changes in the natural rate of unemploymentare inconsistent with theories in which the natural rate is independent of aggregate demand. Regardless of theexplanation that is put forward, however, our results provide additional evidence on the persistent nature ofemployment that reflect other findings in the literature.

15

Figure 1: Expectation and Coefficient of Variation of the First Passage Times between U andD States based on IP Growth

Figure 2: Expectation and Coefficient of Variation of the First Passage Times between U andD States based on Employment Growth

passage times also show such similarity. Typically these countries benefit from geographicalproximity and their participation in the European Union provides an organizational proxim-

16

ity. As we already noted, the exceptions include Spain and the UK. For Spain, the expectedpassage time for both IP and employment growth tend to be longer than most of the countriesin our sample. For the UK, it is the behavior of employment growth that differentiates it fromthe remaining developed countries.

For Asian countries, we cannot talk about a systematically organized political, economicand monetary union like the one that exists in Europe. However, the 21st century has broughtrapid integration of Asian economy and the emergence of what can be termed an informal“Asian Union” (see Gresser, 2004). These observations justify the similarities that we observein the estimated processes for IP growth for Asian countries such as China, Japan, SouthKorea, Philippines, and Malaysia. Finally, we observe similarities in employment growth foremerging economies such as China, the Philippines, Turkey, Malaysia, and Mexico. The shortexpected passage expected passage times in employment growth for countries such as Malaysia,Mexico and Turkey reflect the existence of crises and institutional and policy changes that limitthe sample period over which stationary processes for employment growth can be fitted.

Figures 1 and 2 also allow us to examine the variability of the first passage times from thedifferent states using their CV. Typically countries such as China, Korea, Mexico have lessvariability in their first passage times from the different states. Turkey stands out as an outlierin terms of its CV for the first passage times, no doubt reflecting the short sample over whichthis measure is computed both for IP and employment growth.

8 Composite indicators

Up to this point, we examined the time-homogeneity and time-dependence properties of impor-tant leading economic indicators such as IP and employment growth of various countries. Onthe other hand, an index composed of more than one leading economic indicator may providea healthier indication of future economic activity. In this section, an index comprised of IPand employment growth is created using the methodology of finite Markov chains describedabove.

Recall that the estimated Markov chains were not necessarily time-homogeneous for all thecountries in our sample. To construct the composite indicators, we first identify the minimumof the two dates for which time homogeneity of the Markov chains for IP and employmentgrowth can be established. Second, we allow for the fact that there may be second-orderdependence in the composite indicator depending on the order of the underlying univariateMarkov chains. If the underlying Markov processes are i.i.d. or of orders one, we constructthe composite indicator as follows: we identify a pair of states H (High) and L (Low) for IPindex growth, and U and D for employment growth. In this framework, there exist four statesfor which the composite indicator can be observed: HU , LU , HD and LD. As an example,if the process is in state LU , this means that IP growth is below average but employmentgrowth above average. On the other hand, if either one of the univariate processes for IPor employment growth are of order two, then the composite indicator is constructed to takeinto account this second-order dependence. For example, suppose that IP growth follows asecond-order process while employment growth follows a first-order process. In this case, therelevant states for the composite indicator are given by UUH, UUL, UDH, UDL, DUH,DUL, DDH, and DDL. Thus, UUL denotes the state in which IP growth has been aboveaverage for the last two periods in a row while employment growth has been below average last

17

Figure 3: Expectation of the First Passage Times between UP-High and Down-Low Statesbased on the Employment Growth-Industrial Production Index Growth Time Series

period. The process can then transit to one of four possible states today, UUH, UUL, DUL,and DUH. There were only three countries for which we estimated second-order processes foreither IP or employment growth, Finland, the Netherlands, and the UK. Let (p, q) denote theorders of IP and employment growth in the composite indicator. As before, we conducted atest of the time dependence of the composite process by testing for the equality of the (2, 1) or(1, 2) processes against a (1, 1) process. We were unable to reject the null hypothesis that thecomposite processes for Finland and the UK are of order (1, 1). By contrast, we could rejectthe (1, 1) process for the Netherlands against a (2, 1) process.

Tables 7 and 8 show the transition probabilities between the possible states for all (1, 1)processes. These tables show that most developed countries as well as developing countriessuch as S. Korea or S. Africa the estimated probabilities that the composite process will remainin the states HU or LD, conditional on starting out in these states, respectively, are highercompared to the probabilities of transiting to the other states. These probabilities are alsotypically higher than the probabilities of remaining in the states HD and LU , conditionalon starting out these states, respectively. When the composite indicator is in state HU , theeconomy is in a period when activity is unambiguously high. Similarly, when the indicator isin state LD, economic activity is unambiguously low. Thus, we find that for many economies,IP growth and employment growth tend to move together, lending credence to the idea ofconsidering their behavior in terms of a composite index. For other countries such as China,Malaysia, Mexico, the Philippines, or Turkey, there is a weaker relationship between IP andemployment growth. For example, for Turkey the probabilities of remaining in the HD or LUstates are higher than remaining in the HU or LD states. This implies that the behavior ofIP growth and employment growth are “de-coupled” from each other, at least over the sample

18

period in question. Furthermore, the probabilities of transiting to the HU state conditional onbeing in the HD or LD states are higher than the probability of remaining in the HU state.This results suggest that the economy exhibits very little persistence. Similar findings occur forother developing economies such as Chile, China, Malaysia, Mexico and the Philippines. In thecase of Turkey, this may have to do with the shortness of the sample. However, the presenceof similar behavior for other developing economies suggests that there are some fundamentaldifferences in the cyclical dynamics of these countries relative to developed ones.

Table 9 presents the p-values for the test of the equality of the composite processes acrossdifferent countries. The findings that we observed in Tables 7 and 8 emerge much more clearlyhere. For countries such as Chile, Mexico, China, Malaysia, the Philippines and Turkey, we canreject at significance levels of 10% or less the hypothesis that these countries have probabilitytransition matrices that are identical to those of others in our sample. These rejections occurespecially relative to the developed countries. Considering the case of China, we can rejectthe equality of probability transition matrices for all countries in Table 9 except Japan, Chile,Mexico, Malaysia, the Philippines and Turkey. For Mexico, there is slightly less evidence ofsuch differences in the cyclical dynamics of the composite indicator. Here we can reject thenull hypothesis of equality against Canada, the UK, the US, France, Germany, Italy, Spain aswell as S. Africa. Indeed Chile, Mexico, China, Malaysia, the Philippines and Turkey appearto comprise one distinct group and the remaining developed countries plus S. Korea and S.Africa comprise another group in terms of their cyclical dynamics. There is some evidencethat the UK composite indicator has different properties than those of some other developedcountries such as the US and France but this is most likely due to the persistent nature of itsemployment process.

In Figure 3, we examine the relation between the estimated passage times between thestates HU and LD for each country. We observe that the estimated passage times betweendifferent phases of economic activity exhibit symmetric behavior for most of the countriesin question, that is, E(THU,LD) and E(TLD,HU ) are similar. What is more, we see that theexpected passage times between the different phases of industrialized economies like Germany,Japan and United States are typically longer than they are for less industrialized countriessuch as Turkey, China and Mexico. However, the expected passage times for the compositeindicator tend to more dispersed than those for the individual indicators, suggesting morevariation across countries in factors that affect IP and employment growth jointly. We observethat Spain continues to exhibit highly persistent behavior in that it has very high expectedpassage times from HU to LD, and vice versa. However, based on the behavior of the compositeindex, the UK economy tends to resemble other developed economies such as Japan, suggestingthat the composite index provides a better summary of cyclical dynamics than the behaviorof individual components separately.

9 Conclusion

In this study, we have used a simple but effective nonparametric testing procedure whichestimates the transition probability distribution of economic time series directly. This testingprocedure does not require any distributional assumptions which are generally involved in theapplication of parametric tests. By following a systematic Markov based testing procedure, werevealed the time-dependence and time-homogeneity properties of industrial production and

19

employment growth of a key set of developed and developing countries.Our results yield some interesting conclusions. First, we find that the processes for both

industrial and employment growth tend to be more stable for developed countries such as theAnglophone and EU countries as well as some newly industrialized countries in East Asia. Bycontrast, the processes for various developing and emerging economies tend to exhibit moreinstability. An important exception to this finding is Japan, which appears to have undergoneimportant changes as a result of the factors that led to the “lost decade” of the 1990’s. Second,we find that the processes for employment growth tend to exhibit greater heterogeneity thanthose for industrial production growth across different countries. This result holds whetherwe consider the developed or the developing countries. In the former, we find evidence foroft-mentioned persistence of employment (or unemployment) growth in countries such as theUK and Spain. More generally, we compare the expected passage times between the highand low economic activity periods for the economic times series in hand to identify commonpatterns across countries. Our analysis shows that the estimated durations of the alternativestates for industrial production and employment growth are very close in European countrieslike Germany, Italy and France. This finding reflects their geographical and organizationalproximity in the European Union, and forms the basis for the notion of a Euro area businesscycle. Similar behavior is also observed in Asian countries like Japan, China, Philippines,Malaysia and South Korea. This is the result not only of their geographical proximity but alsotheir strengthened international economic relationships. Next, we find that a disparate set ofemerging market economies such as China, Mexico, and Turkey share similar characteristics interms of the cyclical dynamics of their industrial production and employment series, suggestingthe importance of underlying institutional and policy factors that transcend simple geograph-ical considerations or trade linkages. Finally, we construct a composite indicator of economicactivity using information on both IP and employment growth. Here we find that the behaviorof IP and employment growth tend to behave similarly for many developed countries. By con-trast, we find that the behavior of IP growth and employment growth are “de-coupled” fromeach other for developing countries such as Chile, China, Malaysia, Mexico, the Philippinesand Turkey, at least over the sample period in question. This finding is suggestive of a morecomplex set of factors that determine the IP and employment series jointly. Such factors maybe related to the phenomenon of “jobless growth” and the process of structural transformationthat such economies have been undergoing.

20

A First Passage Time Analysis

Once a time series is represented as a time-homogeneous Markov chain with a determinedorder of u, various measures can be calculated by using a finite state Markov chain analysis,e.g. see (Kemeny and Snell, 1976) or (Ross, 2003). The steady state probabilities πi satisfy

∑j

πj = 1,

πj =∑

i

πipij ,

πj ≥ 0, j ∈ Su. (7)

The row vector of steady-state probabilities is π. The time to switch from state U to state Dand from state D to state U can be determined by using a first passage analysis.

Let Ti,j be the first passage time from state i to state j. Let M = {E(Ti,j)} be the matrixof expected first passage times and M2 = {V ar(Ti,j)} be the matrix of the variance of thefirst passage times. Kemeny and Snell (1976) give M and M2 in closed form by using thefundamental matrix Z given as

Z = (I − (P −Π))−1 (8)

where Π is a matrix constructed by π in its each row.Then the expected first passage time matrix is

M = (I − Z + EZdiag)D (9)

where I is the identity matrix, E is a matrix of ones, D is a diagonal matrix with 1/πi as itsDi,ith element, Z is the fundamental matrix, and Zdiag is a diagonal matrix that contains thediagonal elements of Z.

The matrix of the variance of the first passage time is given as

M2 = M(2ZdiagD − I) + 2(ZM − E(ZM)diag)−M2. (10)

The first passage time analysis for the first- and second-order Markov chains are given asspecial cases next.

A.1 First-order Markov chain

Let the probability transition matrix for a stochastic process following a first-order Markovchain with the state space S = {U,D} is given as:

P =

[pU,U 1− pU,U

pD,U 1− pD,U

].

The probability that the first passage time from state U to state D in period k is:

P (TU,D = t) = pU,Ut−1(1− pU,U ).

21

The expected first passage time from state U to state D is thus as follows:

E(TU,D) =1

1− pU,U.

Similarly the variance of the expected first passage time from state U to state D is

V ar(TU,D) =pU,U

(1− pU,U )2.

Consequently, the coefficient of variation of the first passage time from state D to state U is

cv(TU,D) =√

pU,U .

Similarly, the expectation, variance and the coefficient of variation of the first passage timefrom state D to state U are as follows:

E(TD,U ) =1

pD,U,

V ar(TD,U ) =(1− pD,U )

p2D,U

,

cv(TD,U ) =√

1− pD,U .

A.2 Second-order Markov chain:

The transition probability matrix for a stochastic process following a second-order Markovchain with the state space {UU, DU, UD, DD} is given as:

P =

pUU,UU 0 pUU,UD 0pDU,UU 0 pDU,UD 0

0 pUD,DU 0 pUD,DD

0 pDD,DU 0 pDD,DD

. (11)

Using the above transition matrix, let the matrix QU stand for the transient matrix for transi-tion between the up states, i.e., UU and DU . Similarly, let matrix QD represent the transientmatrix for transitions between the down states, i.e., UD and DD. Similarly, let the matrixRU stand for the transient matrix for transition from the up states to the down states, andsimilarly, let matrix QD represent the transient matrix for transitions from the down states tothe up states:

QU =

[pUU,UU 0pDU,UU 0

]and QD =

[pDD,DU 0pUD,DU 0

], (12)

RU =

[pUU,UD 0pDU,UD 0

]and RD =

[pDD,DU 0pUD,DU 0

]. (13)

In this case, the up states include two different states UU and DU and the down statesinclude DU and DD. By using the weighted sum of the first passage times with respect to the

22

likelihood of being in each of these states, Equations (9) and (10) can be written in a simplerway to express the expected first passage times and the variance of the first passage times as

E(TU,D) = πU (I −QU )−2RUu (14)

V ar(TU,D) = 2πU (I −QU )−3QRUu + E(TU,D)− E2(TU,D) (15)

where u = [1, 1]T and πU is the initial probability vector for the up states. By calculating theconditional probabilities in each of the up states UU and DU , πU can be written as

πU =[

πUU

πUU + πDU,

πDU

πUU + πDU

].

Similarly,

E(TD,U ) = πD(I −QD)−2RDu (16)

V ar(TD,U ) = 2πD(I −QD)−3QRDu + E(TD,U )− E2(TD,U ) (17)

where πD is the initial probability vector for the down states. By calculating the conditionalprobabilities in each of the down states UD and DD, πD can be written as

πD =[

πDD

πUD + πDD,

πUD

πUD + πDD

].

B Data

The data sources and sample periods for the countries in the full sample are as follows:

Industrial production:

- Australia, Chile, Finland, France, Germany, Italy, Japan, Mexico, the Netherlands, UK,US 1960:1-2008:2 (IFS)

- Canada, S. Korea, Turkey 1980:1-2008:3 (IFS)

- China 1992:1-2008:2 (IFS)

- Malaysia 1985:1-2008:2 (IFS)

- Philippines 1986:1-2006:1

- S. Africa, Spain 1961:1-2008:1 (IFS)

- Argentina 1994:1-2009:1 (SO)

Total employment

- Australia 1978:1-2009:1 (ILO)

- Canada 1961:1-2009:1 (ILO)

- Japan (ILO), UK (OECD), US 1960:1-2009:1

23

- Germany 1962:1-2008:4 (ILO)

- France, Spain 1980:1-2008:4 (Eurostat); Italy 1980:1-2008:4 (ILO)

- Netherlands 1984:1-2008:3 (ILO)

- Finland 1992:1-2009:1 (ILO)

- Malaysia 1997:1-2009:1 (BIS); S. Korea 1983:1-2009:1 (ILO)

- China 1999:3-2008:3; Philippines 1990:3-2009:1 (ILO);

- S. Africa 1970:1-2p;009:1 (BIS)

- Turkey 2000:1-2009:1 (CB)

- Argentina 1998:3-2009:1 (IFS)

- Chile 1986:1-2009:1; Mexico 2002:2-2009:1 (ILO)

24

References

Alana, L. and P. del-Barrio (2006). “New Revelations about Unemployment Persistence inSpain,” Universidad de Navarra Working Paper no. 10/06.

Altug, S. and M. Bildirici (2010). “Business Cycles around the Globe: A Regime-switchingApproach,” No. 7968 CEPR/EABCN No. 53/2010.

Alvarez, E., F. Ciocchini and K. Konwar (2008). “A Locally Stationary Markov Chain Modelfor Labor Dynamics,” Journal of Data Science 7, 27-42.

Arulampalam, W., A. Booth and M. Taylor (1998). “Unemployment Persistence,” Paperpresented at the CEPR conference on Unemployment Persistence and the Long Run:Evaluating the Natural Rate, Vigo, Spain, November 1997.

Anderson, T. and L. Goodman (1957). “Statistical Inference using Markov Chains,” Annalsof Mathematical Studies 28, 12-40.

Andersson, E. M., D. Bock and M. Frisn (2004). “Detection of Turning Points in BusinessCycles,” Journal of Business Cycle Measurement and Analysis 1, 93-108.

Artis, M., Z. Kontolemis, and D. Osborn (1997). “ Business Cycles for G7 and EuropeanCountries,” Journal of Business 70, 249-279.

Artis, M., H.-M. Krolzig nd J. Toro (2004). “The European Business Cycle,” Oxford EconomicPapers, 46, 1-44.

Ball, L. (2009). “Hysteresis in Unemployment: Old and New Evidence,” NBER WorkingPaper 14818.

Bergoeing, R., P. Kehoe and R. Soto (2001). “A Decade Lost and Found: Mexico and Chilein the 1980’s,” Working Papers Central Bank of Chile 107.

Blanchard, O. and J. Jimeno (1995). “Structural Unemployment: Spain versus Portugal,”The American Economic Review 85 (2), pp. 212-218.

Blanchard, O. and L. Summers (1986) “Hysteresis and the European Unemployment Prob-lem,” In NBER Macroeconomics Annual, Vol 1, Stanley Fischer (ed.), MIT Press, Septem-ber.

Bronfenbrenner, K. and S. Luce (2004). “The Changing Nature of Corporate Global Re-structuring: The Impact of Production Shifts on Jobs in the US, China, and around theGlobe,” US-China Economic and Security Review Commission.

Bry, G. and C. Boschan (1971). Cyclical Analysis of Time Series: Selected Procedures andComputer Programs, National Bureau of Economic Research, New York.

Burns, A. and W. Mitchell (1946). Measuring Business Cycles, National Bureau of EconomicResearch, New York.

Canova, F., M. Ciccarelli, and E. Ortega (2009). “Do Institutional Changes Affect the Busi-ness Cycle? Evidence from Europe,” Bank of Spain.

25

Combes, P-P, T. Mayer and J-F Thisse (2008). Economic Geography: The Integration ofRegions and Nations, University Presses of California, Columbia and Princeton.

De Pace, Pierangelo (2010). “Currency Union, Free-Trade Areas, and Business Cycle Syn-chronization,” manuscript, Pomona College.

Eckstein, Z. and van den Berg, G. (2007). “Empirical Labor Search: A Survey,” Journal ofEconometrics 136, 531-564.

Filardo A. (1994). “Business-Cycle Phases and Their Transitional Dynamics,” Journal ofBusiness and Economic Statistics 12(3), 299-308.

Flinn, C. and Heckman, J. (1982). “New Methods for Analyzing Structural Models of LaborForce Dynamics,” Journal of Econometrics, 18, 115-168.

Gali, J. (1999). “Technology, Employment, and the Business Cycle: Do Technology ShocksExplain Aggregate Fluctuations?,” American Economic Review 89, pp. 249-271.

Giannone, D., M. Lenza, and L. Reichlin (2008). “Business Cycles in the Euro Area,” In A.Alesina and F. Giavazzi (eds.), Europe and the EMU, NBER, forthcoming.

Gresser, E. (2004). “The Emerging Asian Union? China Trade, Asian Investment, and NewCompetitive Challenge,” Policy Report, Progressive Policy Institute. Washington. D.C.

Hamilton, J. (1989). “A New Approach to the Economic Analysis of Nonstationary TimeSeries and the Business Cycle,” Econometrica 57, 357-384.

Harding, D. and A. Pagan (2002a). “A Comparison of Two Business Cycle Dating Methods,”Journal of Economic Dynamics and Control 27, 1681-1690.

Harding, D. and A. Pagan (2002b). “Dissecting the Cycle: A Methodological Investigation,”Journal of Monetary Economics 49, 365-381.

Hodge, D. (2009). “Growth, Employment and Unemployment in South Africa,” South AfricanJournal of Economics 77(4), 488-504.

Hodrick, R. and E. Prescott (1997). “Postwar US Business Cycles: An Empirical Investiga-tion,” Journal of Money, Credit and Banking 29, 1-16.

Kemeny, J. G. and J. L. Snell (1976). Finite Markov Chain, Springer-Verlag, New York.

Kim, C. and C. Nelson (1999). “Friedman’s Plucking Model of Business Fluctuations: Testsand Estimates of Permanent and Transitory Components,” Journal of Money, Creditand Banking, 31(3), Part 1, 317-334.

Kim, C. and C. Piger (2002). “Common Stochastic Trends, Common Cycles, and Asymmetryin Economic Fluctuations,” Journal of Monetary Economics 49, 1189-1211.

Knoben, J. and L. Oerlemans (2006). “Proximity and Inter-organizational Collaboration: ALiterature Review,” International Journal of Management Reviews 8(2), 1-89.

26

Kose, M., G. Meredith and M. Christopher (2004). “How Has NAFTA Affected the MexicanEconomy? Review and Evidence,” IMF Working Papers 04(59).

Lahiri, K. and G. Moore (1992). Leading Economic Indicators: New Approaches and Fore-casting Records, Cambridge University Press, Cambridge.

Meltzer, A. (2001). “Monetary Transmission at Low Inflation: Some Clues from Japan,”Monetary and Economic Studies 19(S-1).

Neftci, S. (1984). “Are Economic Time Series Asymmetric Over the Business Cycle?,” Journalof Political Economy 92, 307-328.

Ross, S. (2003). Introduction to Probability Models, 8th ed. Academic Press, San Diego.

Tan, B. and K. Yilmaz (2002). “Markov Chain Test for Time Dependence and Homogeneity:An Analytical and Empirical evaluation,” European Journal of Operational Research137(3), 524-543.

Tang, M. (2008). “Twin Global Shocks Dent United Kingdom Outlook,” IMF Survey 37(9).

Torre, A. and A. Rallet (2005). “Proximity and Localization,” Regional Studies 39(1), 1-13.

Tiraboschi, M. and M. Del Conte (2004). “Recent Changes in the Italian Labor Law,” Paperpresented in JILPT Comparative Labor Law Seminar, Tokyo, Japan.

Yeldan, E. (2008). “Turkey and the Long Decade with The IMF: 1998-2008,”http://www.networkideas.org/news/jun2008/Turkey-IMF.pdf

27

Country Beginning Order Transition Probabilities Expected PassageYear Times (Quarters)

pU,U pU,D pD,U pD,D E(TU,D) E(TD,U )Australia 1960 1 0.784 0.216 0.228 0.772 4.62 4.38Canada 1980 1 0.855 0.145 0.148 0.852 6.87 6.75Japan 1993† 1 0.816 0.184 0.292 0.708 5.43 3.43UK 1974 2 See (1) below 5.24 4.06USA 1960 1 0.893 0.107 0.154 0.846 9.34 6.50Finland 1960 1 0.742 0.258 0.237 0.763 3.87 4.22France 1960 1 0.796 0.204 0.187 0.813 4.90 5.33Germany 1960 1 0.830 0.170 0.191 0.809 5.88 5.24Italy 1960 1 0.798 0.202 0.170 0.830 4.95 5.88Netherlands 1963† 2 See (2) below 6.73 6.32Spain 1960 1 0.864 0.136 0.096 0.904 7.36 10.40Argentina 1997 1 0.879 0.121 0.174 0.826 8.25 5.75Chile 1960 1 0.869 0.131 0.258 0.742 2.83 3.67Mexico 1995† 1 0.839 0.161 0.227 0.773 6.20 4.40Malaysia 1997† 1 0.818 0.182 0.200 0.800 5.50 5.00S.Korea 1980 1 0.680 0.320 0.267 0.733 3.13 3.75China 1992 1 0.667 0.333 0.292 0.708 3.00 3.43Philippines 1981 1 0.704 0.296 0.250 0.750 3.38 4.00S.Africa 1983 1 0.852 0.148 0.192 0.808 6.75 5.33Turkey 2002† 0 0.482 0.518 0.482 0.518 1.93 2.08† Denotes break year

Table 1: Transition Probabilities and Expected Passage Times: IP Growth

where

(1) P =

0.823 0 0.177 00.522 0 0.478 0

0 0.130 0 0.8700 0.253 0 0.747

and

(2) P =

0.859 0.1410.588 0.412

0.250 0.7500.156 0.844

28

Country Beginning Order Transition Probabilities Expected PassageYear Times (Quarters)

pU,U pU,D pD,U pD,D E(TU,D) E(TD,U )Australia 1978 1 0.892 0.108 0.174 0.826 9.25 5.75Canada 1960 1 0.828 0.172 0.183 0.817 5.82 5.47Japan 1993† 1 0.811 0.189 0.222 0.778 5.29 4.50UK 1975 1 0.944 0.056 0.106 0.894 17.79 9.40USA 1960 1 0.876 0.124 0.177 0.823 8.07 5.64Finland 1992 2 See (3) below 9.39 6.33France 1980 1 0.827 0.173 0.152 0.848 5.78 6.56Germany 1962 1 0.891 0.109 0.121 0.879 9.20 8.27Italy 1993† 1 0.912 0.088 0.111 0.889 11.34 9.00Netherlands 1984 1 0.822 0.178 0.163 0.837 5.62 6.12Spain 1980 1 0.957 0.043 0.071 0.929 22.99 14.01Argentina 2002† 1 0.933 0.067 0.083 0.917 14.99 12.01Chile 1999† 1 0.647 0.353 0.273 0.727 2.83 3.67Mexico 2000 0 0.625 0.375 0.625 0.375 2.67 1.60Malaysia 1997† 0 0.489 0.511 0.489 0.511 1.96 2.05S.Korea 1983 1 0.857 0.143 0.182 0.818 7.00 5.50China 1999 1 0.867 0.133 0.111 0.889 7.50 9.00Philippines 1990 1 0.647 0.353 0.333 0.667 2.83 3.00S. Africa 1970 1 0.821 0.179 0.129 0.871 5.58 7.73Turkey 2000† 0 0.546 0.455 0.545 0.455 2.20 1.83† Denotes break year

Table 2: Transition Probabilities and Expected Passage Times: Employment Growth

where

(3) P =

0.895 0 0.105 0

0.8 0 0.2 00 0.75 0 0.250 0.125 0 0.875

.

Canada US Japan Finland France Germ. Italy Spain Argen. Chile Mexico Malay. S. Kor. China Philip. S. Afr.Austr. 0.27 0.045 0.75 0.79 0.77 0.60 0.58 0.015 0.39 0.23 0.80 0.93 0.35 0.41 0.58 0.51Canada 0.78 0.11 0.11 0.55 0.73 0.64 0.62 0.91 0.32 0.71 0.78 0.03 0.06 0.08 0.85US 0.17 0.007 0.13 0.33 0.17 0.42 0.95 0.26 0.53 0.53 0.002 0.01 0.009 0.65Japan 0.57 0.53 0.57 0.42 0.05 0.48 0.69 0.86 0.78 0.34 0.42 0.46 0.58Finland 0.48 0.26 0.34 0.003 0.19 0.06 0.52 0.75 0.68 0.66 0.89 0.23France 0.85 0.95 0.09 0.54 0.21 0.80 0.98 0.16 0.24 0.35 0.69Germ. 0.81 0.13 0.77 0.43 0.92 0.98 0.07 0.14 0.19 0.93Italy 0.15 0.56 0.15 0.73 0.94 0.11 0.18 0.25 0.68Spain 0.58 0.02 0.26 0.38 0.001 0.007 0.005 0.28Argen. 0.70 0.81 0.77 0.07 0.097 0.13 0.92Chile 0.88 0.68 0.02 0.073 0.06 0.68Mexico 0.25 0.39 0.93 0.94 0.98Malay. 0.44 0.43 0.59 0.90S. Kor. 0.97 0.95 0.07China 0.88 0.12Philip. 0.16

Table 3: p-values for Industrial Production Growth

29

Canada UK US Japan France Germany Italy Nether. Spain Argen. Chile S. Korea China Philip. S. AfricaAustra. 0.49 0.31 0.95 0.45 0.56 0.71 0.72 0.56 0.11 0.63 0.05 0.83 0.78 0.003 0.38Canada 0.02 0.62 0.88 0.89 0.23 0.31 0.96 0.006 0.34 0.17 0.89 0.13 0.02 0.61UK 0.13 0.04 0.07 0.42 0.82 0.07 0.79 0.96 0.002 0.13 0.0005 0.000 0.05US 0.55 0.66 0.55 0.60 0.67 0.04 0.54 0.06 0.94 0.03 0.002 0.42Japan 0.73 0.22 0.25 0.81 0.012 0.27 0.41 0.77 0.38 0.18 0.52France 0.48 0.46 0.99 0.03 0.44 0.16 0.84 0.12 0.02 0.92Germany 0.93 0.43 0.20 0.81 0.015 0.53 0.007 0.0003 0.45Italy 0.42 0.58 0.93 0.026 0.53 0.02 0.003 0.44Nether. 0.03 0.41 0.21 0.87 0.16 0.04 0.87Spain 0.93 0.0004 0.04 0.0001 0.0000 0.02Argen. 0.05 0.48 0.04 0.014 0.45Chile 0.13 0.98 0.89 0.098S.Korea 0.09 0.02 0.63China 0.93 0.06Philip. 0.007

Table 4: p-values for Employment Growth

30

Beginning Transition Probabilities Expected PassageYear Times (Quarter)

HU HD LU LD E(THU,LD) E(TLD,HU )Australia 1978 HU 0.739 0 0.196 0.065 12.18 7.47

HD 0.333 0.5 0 0.167LU 0.259 0.037 0.593 0.111LD 0.0625 0.125 0.0625 0.75

Canada 1980 HU 0.818 0 0.114 0.068 11.64 8.18HD 0.364 0.636 0 0LU 0.125 0 0.75 0.125LD 0.033 0.133 0.033 0.8

Japan 1992 HU 0.72 0.08 0.16 0.04 10.81 6.11HD 0.308 0.538 0.077 0.077LU 0.167 0.083 0.5 0.25LD 0.083 0.25 0 0.667

UK 1974 HU 0.083 0.25 0 0.667 17.80 9.22HD 0.15 0.65 0 0.2LU 0.282 0 0.641 0.077LD 0.08 0.24 0 0.68

US 1960 HU 0.831 0.052 0.104 0.013 14.57 11.51HD 0.2 0.65 0 0.15LU 0.194 0 0.548 0.258LD 0.048 0.048 0.097 0.807

Finland 1992 HU 0.636 0.046 0.318 0 14.13 6.79HD 0.636 0.046 0.318 0LU 0.375 0.5 0 0.125LD 0.263 0 0.600 0.157

France 1980 HU 0.714 0.114 0.143 0.029 9.68 10.21HD 0.333 0.278 0 0.389LU 0.267 0 0.533 0.2LD 0 0.220 0.073 0.707

Germany 1962 HU 0.824 0.029 0.132 0.015 14.20 11.49HD 0.214 0.643 0 0.143LU 0.208 0.042 0.5 0.25LD 0.032 0.115 0.05 0.803

Italy 1992 HU 0.727 0.091 0.182 0 18.20 15.43HD 0 0.786 0 0.214LU 0.091 0 0.864 0.045LD 0.083 0.167 0.167 0.583

Spain 1980 HU 0.805 0 0.195 0 26.42 19.00HD 0.077 0.692 0.077 0.154LU 0.25 0 0.643 0.107LD 0 0.148 0.037 0.815

Table 5: Transition Probabilities and Expected Passage Times for the Composite Indicators:Developed Countries

31

Beginning Transition Probabilities Expected PassageYear Times (Quarter)

HU HD LU LD E(THU,LD) E(TLD,HU )Malaysia 1997 HU 0.667 0.25 0 0.083 7.39 9.7

HD 0.3 0.4 0.1 0.2LU 0 0.111 0.444 0.445LD 0.090 0.182 0.364 0.364

Korea 1983 HU 0.677 0.065 0.193 0.065 9.96 8.21HD 0.25 0.375 0.0625 0.3125LU 0.167 0.125 0.625 0.083LD 0.074 0.148 0.074 0.704

Argentina 2001 HU 0.846 0 0.154 0 15.00 12.00HD 0.2 0.6 0 0.2LU 0.5 0 0 0.5LD 0 0.286 0 0.714

Chile 1998 HU 0.5 0.125 0.375 0 6.69 8.05HD 0.333 0.445 0.222 0LU 0.2 0.2 0 0.6LD 0 0.25 0.083 0.667

Mexico 2000 HU 0.455 0.090 0.273 0.182 6.42 2.76HD 0.6 0.4 0 0LU 0.4 0.2 0.2 0.2LD 0.285 0.143 0.143 0.49

China 1999 HU 0.25 0.125 0.125 0.5 2.26 3.57HD 0.4 0.6 0 0LU 0.5 0 0 0.5LD 0.222 0.111 0.111 0.556

Philippines 1990 HU 0.308 0.154 0.308 0.230 5.41 6.20HD 0.353 0.471 0 0.176LU 0.1875 0.125 0.5625 0.125LD 0 0.333 0.25 0.417

S.Africa 1982 HU 0.771 0.114 0.086 0.029 13.47 9.17HD 0.263 0.526 0.053 0.158LU 0.154 0 0.692 0.154LD 0.059 0.147 0 0.794

Turkey 2001 HU 0.25 0 0.375 0.375 3.78 2.40HD 0.4 0.6 0 0LU 0.166 0 0.667 0.167LD 0.428 0.286 0 0.286

Table 6: Transition Probabilities and Expected Passage Times for the Composite Indicators:Developing Countries

32

Can. Japan UK US Fin. France Germ. Italy Spain Argen. Chile Mexico S. Kor. China Malay. Philip. S. Afr. Turk.Austra. 0.81 0.60 0.77 0.27 0.61 0.21 0.78 0.11 0.44 0.75 0.016 0.26 0.79 0.044 0.002 0.055 0.26 0.10Can. 0.36 0.27 0.24 0.23 0.04 0.46 0.08 0.32 0.53 0.007 0.05 0.11 0.03 0.0005 0.003 0.35 0.07Japan 0.24 0.35 0.55 0.35 0.77 0.08 0.17 0.78 0.39 0.53 0.87 0.14 0.20 0.18 0.97 0.20UK 0.01 0.41 0.03 0.11 0.16 0.51 0.80 0.0007 0.023 0.104 0.006 0.0000 0.003 0.17 0.14US 0.39 0.12 0.95 0.22 0.18 0.62 0.006 0.022 0.106 0.007 0.008 0.0006 0.43 0.0009Fin. 0.86 0.56 0.32 0.65 0.79 0.19 0.19 0.43 0.03 0.02 0.34 0.24 0.05France 0.23 0.04 0.09 0.70 0.03 0.04 0.46 0.009 0.02 0.13 0.32 0.002Germ. 0.12 0.42 0.90 0.03 0.06 0.37 0.006 0.005 0.005 0.55 0.002Italy 0.29 0.25 0.0007 0.01 0.17 0.016 0.01 0.02 0.17 0.03Spain 0.89 0.01 0.001 0.08 0.0002 0.0001 0.0005 0.19 0.001Argen. 0.61 0.19 0.44 0.09 0.04 0.08 0.64 0.06Chile 0.42 0.06 0.28 0.05 0.07 0.02 0.02Mexico 0.41 0.96 0.16 0.63 0.05 0.74S.Kor. 0.08 0.09 0.29 0.58 0.06China 0.11 0.36 0.02 0.70Malay. 0.13 0.02 0.01Philip. 0.007 0.27S. Afr. 0.02

Table 7: p-values for the Composite Index

33